I am well aware that the main title was probably produced in AE/Photoshop when the footage was still an ungraded RAW video, but what I don't get is how beautifully integrated and burnt-in it looks, like it was produced at an old-school optical house. This is especially striking to me since most who try to recreate the era in their productions usually film and grade the main footage and work on the credits afterwards, creating a jarringly sharp and sheen-y look that destroys the illusion.

This'll probably be old hat for some of you, but I'm fairly new to AE.

As Tero mentioned, a slight blur (I would use Camera Lens Blur)will soften the edges. I would add a Match Grain effect to better blend in the text. The reason titles look sharp and clean is partly because they lack the grain that video has. Also making sure that you have some color in the title (light pink like the example or whatever other color matches your footage)will help - applying Match Grain to a white title will not do much.

My point was not to use white, but to have some color (does not matter what color) in the elements you want the Match Grain effect applied to. In simple terms: do not use white, use an off white (light gray, or any other color) for titles or graphics that need to be white. If your titles are colored, then there are no issues there. It can be applied to any layer that can take effects.